Glass fiber reinforced polymer (GFRP) composites are becoming more attractive in modern engineering fields due to their outstanding mechanical/physical properties. However, a thorough understanding of their drilling machinability is seriously lacking in the research community. The present work aims to address the drilling behavior of woven GFRP composites under varying cutting speeds and feed rates. Machining studies were conducted using two different diamond-coated special tools involving a double point angle drill and a dagger drill. The drilling machinability of GFRPs was comprehensively analyzed in terms of cutting forces, machining temperatures, drilling-induced damages, dimensional accuracy, and hole wall morphologies. Theoretical analyses and experimental characterizations of delamination damage were conducted for both special drills. A special attempt was made to clarify the impact of different drill shapes on the damage formation and extension of cut GFRP materials. The results obtained can supplement the expertise of composites machining and guide the damage-free drilling of GFRP laminates for academia and industry.